Nonlinear optical techniques, such as SHG, are applied to the conversion of the wavelength of laser light. The use of the SHG, which is capable of reducing the wavelength of laser light, increases recording density in optical recording and reproduction using a laser beam and magnetooptic recording and reproduction.
Phase matching conditions must be satisfied between the fundamental wave and the second higher harmonic for efficient nonlinear optical interaction. However, since the refractive index of optical materials, in general, is dependent on wavelength (dispersion occurs in optical materials), optical materials are unable to satisfy conditions for phase matching between the fundamental wave and the second higher harmonic.
In a periodic inverted-domain structure of a nonlinear ferroelectric optical bulk having domains of nonlinear optical coefficient of periodic inverted signs, it is known that waves produced by the nonlinear polarization of the layers are of the same phase and intensify each other when the thickness of the layers is equal to the product of the coherence length (a length where the phase mismatching angle is .pi.). Such knowledge is disclosed in, for example, J. A. Armstrong, N. Bloembergen, J. Ducuing and P. S. Pershan, Physical Review. 127, (1962), pp. 1918 .about., and D. Feng, N. B Ming, J. F. Hong et al., Applied Physics Letters, 37, (1980), pp. 607-609. Accordingly, materials incapable of direct phase matching, and the maximum nonlinear sensitivity tensor component d.sub.33, which could not have been utilized, can be utilized.
On the other hand, the employment of an optical waveguide structure enables the confinement of light in a waveguide at a high energy density and enables the propagation of light for a long distance in a high energy-density state. However, since the dispersion in the material is significant, it is difficult to match the phases of the fundamental wave and the second higher harmonic.
A SHG using the Cerenkov radiation of a nonlinear waveguide is disclosed in Applied Physics, 56 (1987), pp. 1637-1641, and P. K. Tien, R. Ulrich and R. J. Martin, Applied Physics Letters, 17, (1970), pp. 447 .about.450. This SHG intensifies waves produced by nonlinear polarization with a Cerenkov angle of .alpha. so as to satisfy phase matching automatically and radiates the intensified waves. According)y, a SHG employing a substrate formed of a material having a high nonlinear optical constant is expected to operate at a high efficiency. The nonlinear waveguide SHG of Cerenkov radiation type disclosed in the former reference (Applied Physics) uses the maximum nonlinear sensitivity tensor component d.sub.33 of LiNbO.sub.3. The spot pattern, i.e., the far field pattern, of a light beam emitted by the substrate of the SHG of Cerenkov radiation type is a peculiar pattern, such as a crescent spot pattern and hence it is difficult to focus the light beam to the limit of diffraction by an optical lens system. Since the overlap of the fundamental wave and the Cerenkov wave in the waveguide of the waveguide SHG of Cerenkov radiation type affects significantly the efficiency of the SHG, it is desirable that the Cerenkov angle .alpha. is small so that the degree of overlap is large.
The function of the optical waveguide SHG of Cerenkov radiation type will be examined hereinafter. In a waveguide 2 formed on a nonlinear optical substrate 1, a higher harmonic is produced at an angle .alpha. as shown in FIG. 4 when the propagation constant of the guided mode (fundamental wave) in the waveguide 2 is .beta..sub.F, and the propagation constant of a bulk wave (higher harmonic) in the substrate 1 is k.sub.SHS. Then, EQU .DELTA.k=2.beta.F-k.sub.SHS =2k.sub.FO {.beta..sub.F /k.sub.FO)-n.sub.SHS }(1) EQU 2.beta..sub.F =k.sub.SHS .multidot.cos .alpha. (2)
where .DELTA.k is phase mismatching component, k.sub.FO is propagation constant (2.pi./.lambda..sub.F) of the higher harmonic in a vacuum and n.sub.SHS is the refraction index of the substrate with the higher harmonic. Then, EQU cos .alpha.=(.beta..sub.F /k.sub.FO).multidot.n.sub.SHS ( 3) ##EQU1## where n.sub.SHo and n.sub.SHe are the respective refraction indices of an ordinary ray and an extraordinary ray of higher harmonic wavelength.
Condition for propagating the fundamental wave through the waveguide 2 is EQU n.sub.FS .ltoreq..beta..sub.F /k.sub.FO .ltoreq.n.sub.SHS ( 5)
where n.sub.FS and n.sub.FF are the respective refractive indices with the fundamental wave of the substrate 1 and the waveguide 2. Condition for Cerenkov radiation is EQU .beta..sub.F /k.sub.FO .ltoreq.n.sub.SHS ( 6)
When conditions represented by Expressions (5) and (6) are met Cerenkov radiation second harmonic generation occurs. These conditions are shown graphically in FIG. 5, in which the wavelength of the incident light on the LiNbO.sub.3 waveguide is 1.064 .mu.m (YAG laser light) in the TM mode, the refractive index of the substrate is 2.155 and the refractive index of the waveguide is 2,288. In FIG. 5, refractive index (equivalent refractive index) is measured on the horizontal axis, and the thickness of the waveguide is measured on the vertical axis. When the thickness of the waveguide is not more than about 1.0 .mu.m, a single-mode action is possible. Incidentally, the Cerenkov angle .alpha. on a SHG employing an optical waveguide formed by subjecting the surface of a LiNbO.sub.3 substrate to proton substitution is about 13.degree. when the wavelength of the fundamental wave is 1.064 .mu.m, and is about 16.degree. when the same is 0.83 .mu.m.
If the Cerenkov radiation angle .alpha. in the nonlinear waveguide SHG of Cerenkov radiation type can be reduced, the respective directions of propagation of the fundamental wave and the higher harmonic can be made to coincide with each other, the degree of overlap of the fundamental wave and the higher harmonic can be increased, the conversion efficiency can be improved, and the spot pattern of the output light beam can be improved.
To solve the foregoing problems, the applicant of the present patent application proposed previously an improved SHG as shown in FIG. 2 in Japanese Patent Application No. 63-246545. This SHG comprises a nonlinear ferroelectric optics substrate 1 and an optical waveguide 2 formed on the nonlinear ferroelectric optics substrate 1 and produces a second higher harmonic by Cerenkov radiation. This SHG reduces the Cerenkov angle .alpha. to improve the spot pattern of the second higher harmonic light beam and to improve the conversion efficiency by forming a periodic inverted-domain structure 3 on the substrate 1 and forming an optical waveguide 2 on the periodic inverted-domain structure 3 or by forming a periodic inverted-domain structure 3 in the waveguide 2.
However, such a SHG has many problems in the practical fabrication of the inverted-domain structure 3. A method of alternately inverting domains by controlling current in forming a nonlinear ferroelectric optics crystal by a Czochralski method is disclosed in D. Feng, N. B. Ming, J. F. Hong et al., Applied Physics Letters, 37, 607 (1980); K. Kassau, H. I. Levinstein and G. H. Loiacono, Applied Physics Letters, 6, 228 (1965); and A. Feisst and P. Koidl, Applied Physics Letters, 47, 1125 (1985). This process, however, requires a large-scale equipment and difficult control for micron order domain formation.
Another method of domain inversion diffuse Ti in a nonlinear ferroelectric optics crystal, which, however, entails change in the refractive index of portions in which the domain is inverted, dividing the SH beam into a plurality of beams.
As mentioned above, the conventional method of forming inverted-domain structure is unable to control domains accurately, causes change in the refractive index entailing the division of the second harmonic beam into a plurality of beams, and hence is unable to provide a SHG capable of operating at a high conversion efficiency.